612edo: Difference between revisions
m →Theory: cleanup |
m →Regular temperament properties: crazy update |
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| Line 16: | Line 16: | ||
! rowspan="2" | [[Comma list]] | ! rowspan="2" | [[Comma list]] | ||
! rowspan="2" | [[Mapping]] | ! rowspan="2" | [[Mapping]] | ||
! rowspan="2" | Optimal<br | ! rowspan="2" | Optimal<br>8ve stretch (¢) | ||
! colspan="2" | Tuning error | ! colspan="2" | Tuning error | ||
|- | |- | ||
| Line 24: | Line 24: | ||
| 2.3.5 | | 2.3.5 | ||
| {{monzo| 1 -27 18 }}, {{monzo| -53 10 16 }} | | {{monzo| 1 -27 18 }}, {{monzo| -53 10 16 }} | ||
| {{ | | {{Mapping| 612 970 1421 }} | ||
| +0.0044 | | +0.0044 | ||
| 0.0089 | | 0.0089 | ||
| Line 31: | Line 31: | ||
| 2.3.5.7 | | 2.3.5.7 | ||
| 2401/2400, 4375/4374, {{monzo| -53 10 16 }} | | 2401/2400, 4375/4374, {{monzo| -53 10 16 }} | ||
| {{ | | {{Mapping| 612 970 1421 1718 }} | ||
| +0.0210 | | +0.0210 | ||
| 0.0297 | | 0.0297 | ||
| Line 38: | Line 38: | ||
| 2.3.5.7.11 | | 2.3.5.7.11 | ||
| 2401/2400, 3025/3024, 4375/4374, {{monzo| 21 -6 -7 -2 3 }} | | 2401/2400, 3025/3024, 4375/4374, {{monzo| 21 -6 -7 -2 3 }} | ||
| {{ | | {{Mapping| 612 970 1421 1718 2117 }} | ||
| +0.0363 | | +0.0363 | ||
| 0.0406 | | 0.0406 | ||
| Line 45: | Line 45: | ||
| 2.3.5.7.11.13 | | 2.3.5.7.11.13 | ||
| 2200/2197, 2401/2400, 3025/3024, 4096/4095, 4375/4374 | | 2200/2197, 2401/2400, 3025/3024, 4096/4095, 4375/4374 | ||
| {{ | | {{Mapping| 612 970 1421 1718 2117 2265 }} | ||
| +0.0010 | | +0.0010 | ||
| 0.0871 | | 0.0871 | ||
| Line 52: | Line 52: | ||
| 2.3.5.7.11.13.19 | | 2.3.5.7.11.13.19 | ||
| 1331/1330, 1540/1539, 2200/2197, 2376/2375, 2926/2925, 4096/4095 | | 1331/1330, 1540/1539, 2200/2197, 2376/2375, 2926/2925, 4096/4095 | ||
| {{ | | {{Mapping| 612 970 1421 1718 2117 2265 2600 }} | ||
| −0.0168 | | −0.0168 | ||
| 0.0917 | | 0.0917 | ||
| Line 64: | Line 64: | ||
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | |+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | ||
|- | |- | ||
! Periods<br | ! Periods<br>per 8ve | ||
! Generator* | ! Generator* | ||
! Cents* | ! Cents* | ||
! Associated<br | ! Associated<br>ratio* | ||
! Temperaments | ! Temperaments | ||
|- | |- | ||
| Line 86: | Line 86: | ||
| 162.75 | | 162.75 | ||
| 1125/1024 | | 1125/1024 | ||
| [[ | | [[Crazy]] | ||
|- | |- | ||
| 4 | | 4 | ||
| 194\612<br | | 194\612<br>(41\612) | ||
| 380.39<br | | 380.39<br>(80.39) | ||
| 81/65<br | | 81/65<br>(22/21) | ||
| [[Quasithird]] | | [[Quasithird]] | ||
|- | |- | ||
| 9 | | 9 | ||
| 133\612<br | | 133\612<br>(25\612) | ||
| 315.69<br | | 315.69<br>(49.02) | ||
| 6/5<br | | 6/5<br>(36/35) | ||
| [[Ennealimmal]] | | [[Ennealimmal]] | ||
|- | |- | ||
| 12 | | 12 | ||
| 124\612<br | | 124\612<br>(22\612) | ||
| 243.137<br | | 243.137<br>(43.14) | ||
| 3145728/2734375<br | | 3145728/2734375<br>(?) | ||
| [[Magnesium]] | | [[Magnesium]] | ||
|- | |- | ||
| 12 | | 12 | ||
| 254\612<br | | 254\612<br>(1\612) | ||
| 498.04<br | | 498.04<br>(1.96) | ||
| 4/3<br | | 4/3<br>(32805/32768) | ||
| [[Atomic]] | | [[Atomic]] | ||
|- | |- | ||
| 17 | | 17 | ||
| 127\612<br | | 127\612<br>(17\612) | ||
| 249.02<br | | 249.02<br>(33.33) | ||
| {{monzo| -23 5 9 -2 }}<br | | {{monzo| -23 5 9 -2 }}<br>(100352/98415) | ||
| [[Chlorine]] | | [[Chlorine]] | ||
|- | |- | ||
| 18 | | 18 | ||
| 127\612<br | | 127\612<br>(9\612) | ||
| 249.02<br | | 249.02<br>(17.65) | ||
| 231/200<br | | 231/200<br>(99/98) | ||
| [[Hemiennealimmal]] (11-limit) | | [[Hemiennealimmal]] (11-limit) | ||
|} | |} | ||
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[ | <nowiki/>* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[normal lists|minimal form]] in parentheses if distinct | ||
== Music == | == Music == | ||